Principal components analysis (PCA) has been widely used in many applications, particularly, data compression. Independent component analysis (ICA) has been also developed for blind source separation along with many other applications such as channel equalization, speech processing. Recently, it has been shown that the ICA can be also used for hyperspectral data compression. This paper investigates these two transforms in hyperspectral data compression and further evaluates their strengths and weaknesses in applications of target detection, mixed pixel classification and abundance quantification. In order to take advantage of the strengths of both transform, a new transform, called mixed PCA/ICA transform is developed in this paper. The idea of the proposed mixed PCA/ICA transform is derived from the fact that it can integrate different levels of information captured by the PCA and ICA. In doing so, it combines m principal components (PCs) resulting from the PCA and n independent components (ICs) generated by the ICA to form a new set of (m+n) mixed components used for hyperspectral data compression. The resulting transform is referred to as mixed (m,n)-PCA/ICA transform. In order to determine the total number of components, p needed to be generated for the mixed (m,n)-PCA/ICA transform, a recently developed virtual dimensionality (VD) is introduced to estimate the p where p = m + n. If m = p and n = 0, then mixed (m,n)-PCA/ICA transform is reduced to PCA transform. On the other hand, if m = 0 and n = p, then mixed (m,n)-PCA/ICA transform is reduced to ICA. Since various combinations of m and n have different impacts on the performance of the mixed PCA/ICA spectral/spatial compression in applications, experiments based on subpixel detection and mixed pixel quantification are conducted for performance evaluation.